Question: Simplify the following expression: $\sqrt{5}-\sqrt{45}+\sqrt{125}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{5}-\sqrt{45}+\sqrt{125}$ $= \sqrt{5}-\sqrt{9 \cdot 5}+\sqrt{25 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{5}-\sqrt{9} \cdot \sqrt{5}+\sqrt{25} \cdot \sqrt{5}$ $= \sqrt{5}-3\sqrt{5}+5\sqrt{5}$ Finally, simplify by combining the terms. $= ( 1 - 3 + 5 )\sqrt{5} = 3\sqrt{5}$